This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense <EM>tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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Kevin M. Pilgrim
Combinations of Complex Dynamical Systems
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Author Kevin M. Pilgrim Department of Mathematics Indiana University Bloomington, IN 47401, USA e-mail:
[email protected]
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Mathematics Subject Classification (2000): 37F20 ISSN 0075-8434 ISBN 3-540-20173-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts th